Theorem bianbi

Description: Exchanging conjunction in a biconditional. (Contributed by Peter Mazsa, 31-Jul-2023)

	Ref	Expression
Hypotheses	bianbi.1	|- ( ph <-> ( ps /\ ch ) )
	bianbi.2	|- ( ps <-> th )
Assertion	bianbi	|- ( ph <-> ( th /\ ch ) )

Proof

Step	Hyp	Ref	Expression
1		bianbi.1	|- ( ph <-> ( ps /\ ch ) )
2		bianbi.2	|- ( ps <-> th )
3	2	anbi1i	|- ( ( ps /\ ch ) <-> ( th /\ ch ) )
4	1 3	bitri	|- ( ph <-> ( th /\ ch ) )